Canonical analysis of two convex polyhedral cones and applications

Canonical analysis of two convex polyhedral cones consists in looking for two vectors (one in each cone) whose square cosine is a maximum. This paper presents new results about the properties of the optimal solution to this problem, and also discusses in detail the convergence of an alternating least squares algorithm. The set of scalings of an ordinal variable is a convex polyhedral cone, which thus plays an important role in optimal scaling methods for the analysis of ordinal data. Monotone analysis of variance, and correspondence analysis subject to an ordinal constraint on one of the factors are both canonical analyses of a convex polyhedral cone and a subspace. Optimal multiple regression of a dependent ordinal variable on a set of independent ordinal variables is a canonical analysis of two convex polyhedral cones as long as the signs of the regression coefficients are given. We discuss these three situations and illustrate them by examples.     

Stimulus effects on concurrent performance in transition

Six experimentally naive pigeons were exposed to concurrent variable-interval variable-interval schedules in a three-key procedure in which food reinforcement followed pecks on the side keys and pecks on the center key served as changeover responses. In Phase 1, 3 birds were exposed to 20 combinations of five variable-interval values, with each variable-interval value consistently associated with a different color on the side keys. Another 3 pigeons were exposed to the same 20 conditions, but with a more standard procedure that used a nondifferential discriminative stimulus on the two side keys throughout all conditions. In Phase 2, the differential and nondifferential stimulus conditions were reversed for each pigeon. Each condition lasted for one 5-hr session and one subsequent 1-hr session. In the last 14 conditions of each phase, the presence of differential discriminative stimuli decreased the time necessary for differential responding to develop and increased the sensitivity of behavior to reinforcement distribution in the 1st hr of training; during the last hours of training in each condition, however, the effects of the differential discriminative stimuli could not be distinguished from the effects of reinforcement distribution per se. These results show the importance of studying transitions in behavior as well as final performance. They may also be relevant to discrepancies in the results of previous experiments that have used nonhuman and human subjects.     

SPELLING AND EMERGENT PICTURE-PRINTED WORD RELATIONS ESTABLISHED WITH DELAYED IDENTITY MATCHING TO COMPLEX SAMPLES

Students with academic deficits learned delayed matching-to-sample tasks that used complex sample stimuli, each consisting of a picture and a printed word. A touch to the sample complex removed it from the computer display and produced either picture comparisons or a choice pool of letters. If the comparisons were pictures, selecting the picture identical to the preceding sample was reinforced. If the letters appeared, letter-by-letter construction of the preceding printed word sample was reinforced. The procedure engendered new constructed-response spelling performances and arbitrary relations among pictures and printed words in matching to sample. The emergence of relations among different sets of printed words (paired with the same pictures) suggested classes of equivalent stimuli. Outcome tests involving spoken words as sample stimuli suggested expansion of subjects' spelling repertoires and stimulus classes.     

USING STIMULUS EQUIVALENCE PROCEDURES TO TEACH NAME-FACE MATCHING TO ADULTS WITH BRAIN INJURIES

On pretests, 3 men with brain injuries matched dictated names of three therapists to written names, but did not match dictated or written names to photos, produce correct names in response to photos, locate offices given written names, or name therapists on sight. Match-to-sample training established conditional relations between dictated names and photos. Posttests showed the emergence of untrained conditional relations involving photos and written names, indicating development of three classes of equivalent stimuli (each containing a dictated name, photo, and written name). For 1 participant, conditional relations involving photos of office nameplates were also examined, but did not emerge pre- or posttraining. Two participants produced names orally when given photos and sorted written names and faces together after training; the 3rd participant was unavailable for these posttests. After training, 1 participant located and named all three therapists in their offices.     

PROMOTING STIMULUS CONTROL WITH TEXTUAL PROMPTS AND PERFORMANCE FEEDBACK FOR PERSONS WITH MILD DISABILITIES

We assessed whether written task analyses would serve as textual prompts for performing functional tasks by persons with mild disabilities. Several variables that could influence the effectiveness of textual prompts to promote stimulus control were examined across four groups. A consistent finding was that written specific task analyses combined with end-of-trial performance feedback were effective for promoting the acquisition and generalization of several tasks. Performance transferred immediately to natural discriminative stimuli when the written task analyses and feedback were withdrawn for most tasks and participants. For 2 participants, transfer of stimulus control was accomplished by prompt fading, using individualized written task analyses either with or without performance feedback (Group 1). When feedback was not provided, the effectiveness of written specific task analyses was inconsistent across groups. In contrast to the controlling effects of written specific task analyses, written generic task analyses, which specified only major task outcomes, when combined with performance feedback (Group 1) did not control responding. Overall, this research demonstrated the effectiveness of written specific task analyses and performance feedback to promote stimulus control for persons with mild disabilities.     

Fixed-ratio pausing: Joint effects of past reinforcer magnitude and stimuli correlated with upcoming magnitude

Pigeons responded on fixed-ratio schedules ending in small or large reinforcers (grain presentations of different duration) interspersed within each session. In mixed-schedule conditions, the response key was lit with a single color throughout the session, and pausing was directly related to the past reinforcer (longer pauses after large reinforcers than after small ones). In multiple-schedule conditions, different colors accompanied the ratios ending in small and large reinforcers, and pausing was affected by the upcoming reinforcer as well as the past one. Pauses were shorter before large reinforcers than before small ones, but they continued to be longer after large reinforcers than after small ones. The influence of the past reinforcer was modulated by the magnitude of the upcoming reinforcer; in the presence of the stimulus before the small reinforcer, the effect of the past reinforcer was enhanced relative to its effect in the stimulus before the large reinforcer. These results show that pausing between ratios is jointly determined by two competing factors: past conditions of reinforcement and stimuli correlated with upcoming conditions.     

Examining differential item functioning due to item difficulty and alternative attractiveness

A method for analyzing test item responses is proposed to examine differential item functioning (DIF) in multiple-choice items through a combination of the usual notion of DIF, for correct/incorrect responses and information about DIF contained in each of the alternatives. The proposed method uses incomplete latent class models to examine whether DIF is caused by the attractiveness of the alternatives, difficulty of the item, or both. DIF with respect to either known or unknown subgroups can be tested by a likelihood ratio test that is asymptotically distributed as a chi-square random variable.     

An automated test development of parallel tests from a seed test

Binary programming models are presented to generate parallel tests from an itembank. The parallel tests are created to match item for item an existing seed test and match user supplied taxonomic specifications. The taxonomic specifications may be either obtained from the seed test or from some other user requirement. An algorithm is presented along with computational results to indicate the overall efficiency of the process. Empirical findings based on an itembank for the Arithmetic Reasoning section of the Armed Services Vocational Aptitude Battery are given.The Office of Naval Research, Program in Cognitive Science, N00014-87-C-0696 partially supported the work of Douglas H. Jones. The Rutgers Research Resource Committee of the Graduate School of Management partially supported the work of Douglas H. Jones and Ing-Long Wu. A Thomas and Betts research fellowship partially supported the work of Ing-Long Wu. The Human Resources Laboratory, United States Air Force, partially supported the work of Ronald Armstrong. The authors benefited from conversations with Dr. Wayne Shore, Operational Technologies, San Antonio, Texas. The order of authors' names is alphabetical and denotes equal authorship.     

Delayed constructed-response identity matching improves the spelling performance of students with mental retardation

We assessed the effects of a computerized matching-to-sample procedure on the spelling performances of three students with mental retardation. Initially, the students could 1) match pictures and printed words to one another, and 2) match pictures and printed words to spoken words. However, they could not construct words to either pictures or spoken words (e.g., touch, in order, the letters s->h->o->e given the spoken-word sample Shoe). Word constructions then improved markedly after exposure to delayed constructed-response identity matching (e.g., touch the letters s->h->o->e given the printed-word sample shoe). One subject's oral and written spelling also improved. The results extend previous research by showing multiple positive effects of a computerized spelling intervention. These effects may have occurred in part because of the formation of stimulus classes among pictures, printed words, and spoken words.     

School adjustment, school performance and peer relations among first-graders in a Swedish suburban area

A study of 95 first-graders in one school management area used teacher ratings of problems and sociometric ratings to assess school adjustment and peer relations; 14% of the children had difficulties in reading/writing, motor skill, concentration and psychosocial function. Behavioural problems did not generally coincide with poor scholastic performance, but a small group (6.3%) exhibited problems in both reading/writing, concentration, gross and fine motor skill and psychosocial functions. Sociometric results showed only moderate agreement with teacher ratings. Extremely popular boys had no teacher-rated problems, but children with teacher-rated problems did not to any high degree tend to be isolated. Poor gross motor skill did distinguish isolated boys from others, a relationship that was not evident among the girls. The need to study the validity of teacher ratings as well as the prognostic value of school adjustment in first grade was stressed.